Exceptional magic angles in non-Hermitian twisted bilayer graphene

Twisted bilayer graphene (TBG) features strongly correlated and topological phases due to its flat bands emerging near the magic angle. However, the effects of the non-Hermiticity, arising from the coupling to the environment and dissipation, have remained unexplored. We here develop a simple non-Hermitian (NH) version of twisted bilayer graphene (TBG) by considering relative twisting of two NH graphene monolayers with non-Hermiticity encoded in the imbalance of in-plane nearest-neighbor hopping amplitudes. Remarkably, by generalizing the Bistritzer-MacDonald approach to NH systems, we discover exceptional magic angles where the band structure changes from purely real to purely imaginary thus featuring flat bands with infinite lifetime. Between them, the bands remain flattened, and a Hermitian magic angle emerges at which the imaginary part of energy is maximal, and corresponds to the usual magic angle in non-dissipative, purely Hermitian TBG. We propose an optical lattice setup with gain and loss where our theoretical predictions can be verified. These results suggest the robustness of the flat bands in open systems, paving the way for the further studies on the interplay of dissipative effects, electronic topology, and interactions in such NH moir\'e bands.